European Journal of Mathematics and Statistics

Introduction to the Thukral-Determinantal Formula for Accelerating Convergence of Sequence

Rajinder Kumar Thukral — 2024-06-10

There are two objectives for this paper. Firstly, we shall introduce the Thukral-determinantal formula, and secondly, we shall demonstrate the similarities between the well-established algorithms, namely the Aitkin Δ²algorithm and the Durbin sequence transformation. In fact, we have found that the solution of the Thukral-determinantal formula is equivalent to the Thukral-sequence transformation formula.

Representations of Group Algebras of Non-Abelian Groups of Orders p3, for a Prime p ≥ 3

Nabila M. Bennour — 2024-03-11

In this paper, semidirect products are used to find the matrix representations of group algebras of non-abelian groups of order p³, for a prime p ≥ 3.

Comparative Analysis of GARCH-Based Volatility Models of Financial Market Volatility: A Case of Nairobi Security Market PLC, Kenya

Teddy Mutugi Wanjuki — 2024-08-05

This paper conducted a comprehensive comparative analysis of various GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models to forecast financial market volatility, with a specific focus on the Nairobi Stock Exchange Market. The examined models include symmetric and asymmetric GARCH types, such as sGARCH, GJR-GARCH, AR (1) GJG-GARCH, among others. The primary objective is to identify the most suitable model for capturing the complex dynamics of financial market volatility. The study employs rigorous evaluation criteria, including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Mean Error (ME), and Root Mean Absolute Error (RMAE), to assess the performance of each model. These criteria facilitate the selection of the optimal model for volatility forecasting. The analysis reveals that the GJR-GARCH (1,1) model emerges as the best-fit model, with AIC and BIC values of −5.5008 and −5.4902, respectively. This selection aligns with the consensus in the literature, highlighting the superiority of asymmetric GARCH models in capturing volatility dynamics. The comparison also involves symmetric GARCH models, such as sGARCH (1,1), and other asymmetric models like AR (1) GJG-GARCH. While these models were considered, the GJR-GARCH (1,1) model demonstrated superior forecasting capabilities. The study emphasizes the importance of accurate model selection and the incorporation of asymmetry in volatility modeling. The research provides essential insights into financial market volatility modeling and forecasting using both asymmetric and symmetric GARCH models. These findings have significant implications for government policymakers, financial institutions, and investors, offering improved tools for risk assessment and decision-making during periods of market turbulence.

Iterative Procedure for Finite Family of Total Asymptotically Nonexpansive Maps (TAN)

Agatha Chizoba Nnubia — 2023-09-18

In this paper, CQ Algorithms for iterative approximation of a common fixed point of a finite family of nonlinear maps were introduced and sufficient conditions for the strong convergence of this process to a common fixed point of the family of Total asymptotically Nonexpansive maps (TAN) were proved.

A Heat Transfer Problem with a Velocity Slip in Porous Media: A Galerkin Approach

Khaja Moinuddin — 2023-11-20

In this paper a steady flow of a viscous fluid of finite depth in a porous medium over a fixed horizontal, impermeable bottom with a velocity slip is studied. A Galerkin Method of solution is considered to solve Momentum and Energy equations as the truncation errors both in general and special cases may result in complex situations to get the analytical form of solutions. Using the obtained velocity profile, the Temperature, Mean velocity, Mean Temperature, and heat transfer rates (Nusselt Number) on the free surface as well as on the bottom plate are obtained. The effect of velocity slip in the obtained fields is studied wherever possible. A special case of low porosity is studied and the results are illustrated graphically.